Actually it appears we're mistaken & you can!
http://www.problemneighbours.co.uk/rights-trees-and-overhanging-branches.htmlOverhanging Branches If the branches of a neighbour’s tree start to grow over to your side, you can cut them back to the boundary point between you and your neighbour’s property, as long as the tree is not under a tree preservation order. If it is, you’ll need to seek further clarification. However, the branches and any fruit on them which you may have cut down on your side still belong to the tree owner so they can ask you to return them.
Alternatively, you can return them and ask your neighbour to dispose of them themselves should you wish to do so. What might seem a bit of a strange anomaly, however, is that even though any leaves from your neighbour’s tree may fall into your garden in autumn, you have no right to ask them to come around and sweep them up.